Changes of fixation are made by rapid eye movements, called saccades, that have high velocities and abrupt endings. Disease or injury can interfere with the correct balance between the innervation and muscles and cause the eyes to drift after each saccade, interfering with clear vision. Earlier work in human patients and monkeys has shown that the post-saccadic ocular drift associated with peripheral ocular motor weakness can be corrected by a central neural mechanism within a few days. It has been proposed that this adaptive mechanism operates by adjusting the ratio of the phasic and tonic components (the pulse and step) of saccadic innervation. The suppression of post-saccadic ocular drift was studied in normal monkeys by optically inducing retinal image slip after every saccade. It was found that retinal slip alone was sufficient to elicit post-saccadic drift suppression. It was also discovered that the time constant of the ocular drift's waveform depended on the time constant of the optically imposed image slip. Simulation of these results with a mathematical model of the saccadic system led to the conclusion that the saccadic innervation must consist of three parts, with a transition component (or slide) being added between the phasic and tonic components. Analysis of the model showed that three factors had to be controlled to achieve adaptive suppression of post-saccadic ocular drift: the gain of the step of innervation, and both the gain and the time constant of the slide of innervation.